Simplify the following expression: $r = \dfrac{z^2 - 10z + 21}{z - 3} $
First factor the polynomial in the numerator. $ z^2 - 10z + 21 = (z - 3)(z - 7) $ So we can rewrite the expression as: $r = \dfrac{(z - 3)(z - 7)}{z - 3} $ We can divide the numerator and denominator by $(z - 3)$ on condition that $z \neq 3$ Therefore $r = z - 7; z \neq 3$